Finite Group Databasebeta

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C7×Dic9×C127 #44544629

order32004
automorphism?
homologyAbelianization (H1) = C4×C7×C127 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic9×C127
unambiguous semidirect productC9⋊(C4×C7×C127)

Splittings

derived, SylowC9 ⋊ C4×C7×C127
HallC7×C9×C127 ⋊ C4
HallC9×C127 ⋊ C4×C7
HallC7×C9 ⋊ C4×C127

Subgroups

subgroupG/H
center, hypercenterC2×C7×C127D9
commutator, hypocenterC9C4×C7×C127
FrattiniC2×C3D3×C7×C127
FittingC2×C7×C9×C127C2
socle, prime radicalC2×C3×C7×C127D3
cosocleC2×C9C2×C7×C127
LCSG ▷ C9
UCSC1 ◁ C2×C7×C127

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32004

Conjugacy classes & character table

10668 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 11);